23x+1=7/15x+3

Solution for 23x+1=7/15x+3 equation:

23x+1=7/15x+3

We move all terms to the left:

23x+1-(7/15x+3)=0


Domain of the equation: 15x+3)!=0

x∈R


We get rid of parentheses

23x-7/15x-3+1=0

We multiply all the terms by the denominator


23x*15x-3*15x+1*15x-7=0

Wy multiply elements

345x^2-45x+15x-7=0

We add all the numbers together, and all the variables

345x^2-30x-7=0

a = 345; b = -30; c = -7;
Δ = b2-4ac
Δ = -302-4·345·(-7)
Δ = 10560
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10560}=\sqrt{64*165}=\sqrt{64}*\sqrt{165}=8\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{165}}{2*345}=\frac{30-8\sqrt{165}}{690}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{165}}{2*345}=\frac{30+8\sqrt{165}}{690}
$